I wouldn't say that animation fans tend not be interested with drama, more that rarely are they offered anything dramatic. Even in anime, the real straight up dramas show up few and far between. Usually, drama is paired with a psychosuspense, action or comedy element, even in an anime (I'll note though that some of my favorite anime are dramas; Haibane, Koi Kaze and Windy Tales are definitely more drama than any other genre.) In the US, any drama that does show up is either a rare addition to a comedic show, or it's a sidenote in an action toon.
I think if some one made a good animated drama in America, animation fans would atleast give it a shot, and a good few would even enjoy it. Certainly Geneon USA seems to count on US animation fans looking for drama, as some of what they've co-funded is the closest to pure drama that any commercial animation (let's ignore non-commericial work like Film Board of Canada shorts,) has ever been. KoiKaze is romantic drama. Haibane Renmei is crisis-of-faith drama. Both wouldn't exist if a US company hadn't put up a large piece of the money for them. As such, there has got to be some market, and someday, it'll be capitalized on by an American-based writing/animation staff.